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## Friday 30 September 2016

### Conference transcript: 50 Minutes of Action

Last week I spoke for 20 minutes at CASSIS, the Cascadia Symposium of Statistics in Sport, in Vancouver, BC. The other speakers were outstanding, and among the things I gained was a renewed appreciation for geography and the making of maps and graphics. It's something I'm very poor at, and I would very much like to make some contacts that are good at visual analytics. I also got to meet one of the co-creators of nhlscrapr, who has just make a similar program for American football called nflscrapr.

My talk was about the supposed tendency for hockey teams in the NHL to, when tied in the last ten minutes of regulation time, play very conservatively. That is, defensive strategies are adopted by both teams during this time that reduce the number of goals scored for either side, and generally make for very boring play.

At least that was my research hypothesis: fewer goals, shots, and shot attempts in tied situations compared to similar situations where one team is winning.

Why would this happen? Because teams behave rationally. The winning team in a National Hockey League game is awarded 2 points towards earning a place in the playoffs at the end of the season. The losing team, however, is awarded 0 points if the game ends after regulation play (60 minutes), or 1 point if they game ends in overtime or the shootout. That means there are 2 points distributed between the teams in a regulation game, and 3 points in an overtime or shootout game. Assuming the winner of an overtime game is essentially determined by a coin toss, a team that is tied can expect 1.5 points for remaining tied after 60 minutes.

From the 1.5 point perspective, the potential downside of breaking this tie is 3 times as large as the potential upside. We can assume that a team is already doing everything it can to maximize the chance that it scores the next goal simply because winning is better than losing. In other words, if there was a way a team could influence the game to score more goals while preventing the other team from doing the same, they would already be doing it. However, we can't necessarily assume they are doing everything they can to reduce or increase the rate of goal scoring in general.

So my assumption is that teams DO exert this sort of influence on the game.

Consider the rate of goal scoring in the last two years of the 'zero-sum' era, before the extra overtime point was introduced. The black dotted line for tied games follows the same pattern as the rest of the games, up until the last minute or two when teams that are behind by 1 goal tend to pull their goalie for an extra attacker.

In the first two years after the overtime loss point is introduced, we see a divergence, in which tied games show less scoring in the last 10 minutes.

Likewise, we see this again five years later in the first two years after the shootout in introduced, but less pronounced.

But these are old graphs. Is this the same divergence happening now, a decade into the shootout era? Here's the raw goals per hour for the most recent 3 seasons, which is measuring the same thing as the above graphs, but with less smoothing.

Without the smoothing, the empty net effect is concentrated on the last minute of play. For the team that's behind by a goal, it climbs to 8 goals per hour. For the team ahead by one, it climbs to 18 goals per hour.

The divergence between the tied teams and the rest has disappeared into the minute-by-minute noise. Maybe it will show up elsewhere. We can also get the shots and shot attempts per hour, like in this next graph.

With the shot attempts, we see a divergence, but not the one we would have expected from teams necessarily trying to preserve a tie. The worse situation a team is in, the more shot attempts they make. Even tied teams play very aggressively in the last minute. The team that's ahead makes fewer shot attempts, but has higher quality shots. The extreme case of this is in the last minute when the losing team has pulled their goalie - anything that would qualify as a shot is a goal against an empty net. It's possible that teams that are ahead are playing more conservatively because they have less to lose from a tie than the losing team has to gain, but that wasn't the hypothesis at the start.

With the newer data, not only can we get shots and shot attempts, but we can also isolate out the time and events in which a goalie was out of net, or when a team was on the powerplay. The following graphs show the goals and shot attempts for those situations. It's essentially the same story, except for the last minute. The one-ahead and one-behind lines can't be trusted in the last minute because there are very few times when the behind team didn't pull their goalie.

So are there 50 regulation minutes of action in an NHL game or 60? My personal grudge against the asymmetry introduced of the overtime loss rule makes me want to say 50, but I can't seem to back that up with recent data. File this one under negative results.